Research Topics
 Linda J S AllenSummaryAffiliation: Texas Tech University Country: USA Publications
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Publications
 Stochastic epidemic models with a backward bifurcationLinda J S Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042
Math Biosci Eng 3:44558. 2006..For population sizes N=/>1000, the deterministic and stochastic models agree, but for small population sizes the stochastic models indicate that the backward bifurcation may have little effect on the disease dynamics...  Relations between deterministic and stochastic thresholds for disease extinction in continuous and discretetime infectious disease modelsL J S Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Math Biosci 243:99108. 2013..These relations are illustrated, analytically and numerically, in two settings, a general stagestructured model and a vectorhost model applied to West Nile virus in mosquitoes and birds...  A habitatbased model for the spread of hantavirus between reservoir and spillover speciesLinda J S Allen
Texas Tech University, Department of Mathematics and Statistics, Lubbock, TX 79409, USA
J Theor Biol 260:51022. 2009..Environmental changes that result in greater habitat overlap result in more encounters among various species that may lead to pathogen outbreaks and pathogen establishment in a new host...  Mathematical models for hantavirus infection in rodentsLinda J S Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 1042, United States of America
Bull Math Biol 68:51124. 2006..These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels...  Probability of a disease outbreak in stochastic multipatch epidemic modelsGlenn E Lahodny
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Bull Math Biol 75:115780. 2013....  Stochastic models for competing species with a shared pathogenLinda J S Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, United States
Math Biosci Eng 9:46185. 2012..Finally, numerical simulations are conducted to explore the effect of disease on twospecies competition, to illustrate some of the analytical results and to highlight some of the differences in the stochastic and deterministic models...  Disease emergence in multihost epidemic modelsRobert K McCormack
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Math Med Biol 24:1734. 2007..Numerical examples illustrate the dynamics of the two and threehost epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts...  A comparison of persistencetime estimation for discrete and continuous stochastic population models that include demographic and environmental variabilityEdward J Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Math Biosci 196:1438. 2005....  Genetic models for plant pathosystemsJacob C Kesinger
Department of Mathematics and Statistics, Texas Tech University, P O Box 41042, Lubbock, TX 79409 1042, USA
Math Biosci 177:24769. 2002..The original model of Leonard has this same property. However, with random selection values, solutions tend to converge toward the polymorphic equilibrium...  Stochastic models for virus and immune system dynamicsYuan Yuan
Department of Mathematics, Texas Tech University, Lubbock, TX 79409, USA
Math Biosci 234:8494. 2011..It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding...  Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmissionChandrani Banerjee
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Math Biosci Eng 5:61745. 2008..Numerical examples illustrate the dynamics of the models. The biological implications of the results and future research goals are discussed in the conclusion...  Stochastic model of an influenza epidemic with drug resistanceYaji Xu
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
J Theor Biol 248:17993. 2007..Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated...  Coexistence of multiple pathogen strains in stochastic epidemic models with densitydependent mortalityNadarajah Kirupaharan
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Bull Math Biol 66:84164. 2004..The initial number of infected individuals, the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in the stochastic epidemic model...  Basic stochastic models for viral infection within a hostSukhitha W Vidurupola
Texas Tech University, Department of Mathematics and Statistics, Lubbock, Texas 79409 1042, United States
Math Biosci Eng 9:91535. 2012..In addition, the SDE models show significant variability in the timing of the viral peak. The viral peak is earlier for viruses that are released from infected cells via bursting rather than via budding from the cell membrane...  Stability and permanence in gender and stagestructured models for the boreal toadD K Mallawaarachchi
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
J Biol Dyn 5:126. 2011..If ℛ(0)>1 and ℛ(F)<1, then the population becomes diseasefree. However, if both thresholds are greater than one, the population levels are severely reduced by the fungal pathogen...  The basic reproduction number in epidemic models with periodic demographicsCurtis L Wesley
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA
J Biol Dyn 3:11629. 2009..The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains...  Extinction thresholds in deterministic and stochastic epidemic modelsLinda J S Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
J Biol Dyn 6:590611. 2012..In this investigation, we summarize some of the deterministic and stochastic threshold theory, illustrate how to calculate the stochastic thresholds, and derive some new relationships between the deterministic and stochastic thresholds...  A comparison of three different stochastic population models with regard to persistence timeLinda J S Allen
Department of Mathematics and Statistics, Texas Tech University, MS 1042, 117I, Lubbock, TX 79409 1042, USA
Theor Popul Biol 64:43949. 2003..Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth...  The dynamics of two viral infections in a single host population with applications to hantavirusLinda J S Allen
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
Math Biosci 186:191217. 2003..It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus...  A spatially structured metapopulation model with patch dynamicsDashun Xu
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
J Theor Biol 239:46981. 2006..We also derive a stochastic differential equations (SDE) model of the Itô type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model...  Competitive exclusion and coexistence for pathogens in an epidemic model with variable population sizeAzmy S Ackleh
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504 1010, USA
J Math Biol 47:15368. 2003..In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur...  Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasionAzmy S Ackleh
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504 1010, USA
Theor Popul Biol 71:290300. 2007..Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded...